Texas native Jack Conway spent thirteen seasons in professional baseball from 1939 to 1956. The infielder spent three partial seasons in the major leagues with the Cleveland Indians in 1941, 1946 and 1947. Jack was then sold to the New York Giants on January 16, 1948. During these four partial years, Jack appeared in 128 games and picked up 80 base-hits in 359 at-bats for a .223 big league career batting average. Conway also fielded at a .968 percentage during this same period.

His major league career ended on a strange note, when on July 30, 1948, he crashed into teammate Les Layton in right field with two outs in the 9th, allowing a ball hit by Bill Nicholson of the Chicago Cubs to fall safely and Andy Pafko to score from first base. Five days later, after making only one more appearance, he was demoted to the minor leagues and never returned to the Show.

Conway served three seasons (1943-1945) in the Pacific Theater of War with the United States Navy during World War II.

Jack spent twelve seasons in the minor leagues, starting in 1939, with three different teams, and hit for his highest average in his minor league career with a .313 average in 262 at-bats. One could say that Jack's best year in the minors came in 1949 with the AAAIndianapolis Indians of the American Association, when he appeared in 140 games and hit at a .255 clip with 13 home runs. He also fielded the shortstop position at a .957 percentage with just 33 errors in 139 games. He suited up for 859 games during his minor league time and had 3,015 at-bats with 776 base hits, that included 43 home runs, for a minor league career .257 batting average.

Jack managed in the minor leagues for three seasons in 1954-1956. After baseball, he was a house parent for several years at the State Home and at the Methodist Home. For his last ten years, he was a bus driver for Midway Schools. Conway died on January 11, 1993 at Waco, TX. Jack was 74 years of age.